Entry requirements

Probability and Statistics, Several Variable Calculus

Learning outcomes

In order to pass the course (grade 3) the student should

• be able to give an account of the axiomatic foundation of probability theory;
• be able to compute probabilities using combinatorial principles;
• be able to give an account of the concepts of stochastic variable and expected value, and compute probabilities and expected values for given distributions;
• be able to handle conditional probabilities, distributions and expected values;
• know how to use moment generating functions;
• be familiar with applications of the central limit theorem;
• be able to use the Poisson process in stochastic modelling;
• be able to perform computations for simple random walk;
• understand the principles for simulation;
• have a knowledge of probabilistic models in various areas of applications.

Content

Combinatorics. Probability axioms. Calculation of probabilities. Random variables. Probability distributions. Independence and conditional distributions. Expected value and variance, conditional expectations. Moment generating function. Law of large numbers, central limit theory. The Poisson process. Simple random walk. Simulation. Construction of probability models, examples.

Instruction

Lectures and problem solving sessions.

Assessment

Written examination at the end of the course combined with assignments given during the course.